If somebody has eyes for you it means he is interested in you.
If you are hitting it off with somebody that person has been ressponding favorably to you.
Something that is play money is something that you would tend to spend freely.
I guess you could call someone who is involved with a lot of people (especially people of the opposite sex) a playboy. There are other words that are used too. Often those words are not very flattering.
Student or Learner